The Logic of God: A New Look at an Old Reason to Believe – By Joshua Rasmussen

Joshua Rasmussen on A.D. Smith’s Anselm’s Other Argument

A. D. Smith, Anselm’s Other Argument, Harvard University Press, 2014, 256pp., $PRICE
A. D. Smith, Anselm’s Other Argument, Harvard University Press, 2014, 256pp., $49.95

Can belief in God be based upon reason?

Anselm of Canterbury (c. 1033-1109) thought so. Anselm was a Benedictine monk and theologian who became Archbishop of Canterbury in 1093; in philosophy he is most famous for inventing the Ontological Argument for God’s existence. In the Proslogion, Anselm sought to prove God’s reality by reasoning about the concept of God: God, by definition, is the greatest thinkable being — no greater being is even conceivable. Now, a being is surely greater if it exists in reality than if it exists merely in one’s imagination. So, a greatest thinkable being exists in reality. Therefore, God exists — in reality.

This classic argument feels like clever trickery. Is it? Nearly every philosopher since Anselm has considered the argument fallacious. Strangely, however, isolating the precise place where the argument falters has proven rather tricky.

Part of the difficulty is that Anselm offers more than one version of his argument, and objections to one version do not apply to all others. For example, Immanuel Kant famously objects that Anselm errs in thinking that existence is a genuine feature that could contribute to the greatness of a thing. But this objection does no damage to the version of the argument that says that necessary existence is a feature that the greatest thinkable being must possess.

Such multiplicity notwithstanding, many philosophers think that, when we clearly express Anselm’s argument in any of its forms using the language of contemporary logic, we find an ambiguity in the term “God.” Suppose the term “God” is understood as a name that actually picks out an existing entity. Then the argument is circular because the first premise assumes that God exists. Alternatively, we may understand the term “God” as expressing the concept of God. Then the problem is that no mere concept qualifies as the greatest thinkable being — so the argument is unsound.

From the Church of St. Anselm, Bomarzo, Italy. Image via Wikimedia Commons.
From the Church of St. Anselm, Bomarzo, Italy. Image via Wikimedia Commons.

In any case, just about everyone, theist and atheist alike, agrees there is something wrong with Anselm’s classic argument. Enter Anselm’s Other Argument. As his title suggests, A. D. Smith thinks he has found another, better argument buried within the pages of Anselm’s writings. Like one searching for secret treasures, Smith seeks to uncover a new argument for God’s existence. He takes his readers on an expedition in search of gold, sifting to find that nugget he believes just might be a successful argument. In the penultimate chapter, Smith reveals the argument he has been searching for and dusts it off a bit by explaining it in terms of contemporary philosophy and logic.

This other argument has this much in common with the classic version: it moves from a premise about a mere possibility to a thesis about our actual world. Can such reasoning ever be legitimate? One might think that one cannot, in principle, infer what’s actual from what’s merely possible.

Developments in the logic of possibility offer a way forward. Recent work on modal logic has led to a recognized advance. Without going into all the details, we may think of logic as specifying necessary principles of reason. When we apply this conception to the logic of “possibility” and “necessity,” we get a widely accepted and recently developed axiom system, called S5.

The system S5 is designed to capture a foundational and invariable notion of possibility. To illustrate this concept, imagine a mansion whose rooms represent the possible ways reality might have been. You are standing in one of the rooms, with doors to adjacent rooms. These adjacent rooms represent scenarios that are possible relative to your current reality. You can travel to any room in the mansion by going through enough doors. Some rooms are very far away, but each room is directly possible relative to an adjacent room. Each room in the mansion is also possible in a non-relative, fundamental sense, just by being somewhere in the mansion of possibilities. We may say, then, that a scenario is absolutely possible if it could have obtained in some genuinely possible reality. On this understanding of possibility, absolutely possible scenarios cannot fail to be absolutely possible. For suppose a possibility could be impossible. Then this possible impossibility would itself be a room in the mansion, since the mansion contains all possibilities. But this result is contradictory because the mansion contains only possibilities — no impossibilities allowed. In short: whatever is possible cannot be impossible. By similar reasoning, absolutely necessary scenarios cannot fail to be absolutely necessary. Necessity and possibility in this absolute sense are invariable.

With this conception of possibility and necessity in hand, one can, in principle, infer what is actual from what is merely possible. Indeed, logicians have deduced a highly interesting and provocative theorem: if a necessarily-existent reality so much as possibly exists, then such a reality actually exists. For example, if numbers can only exist if they necessarily exist, then if numbers possibly exist, they actually exist. So it is not problematic in principle to argue that something exists from the premise that it possibly exists (in the above, absolute sense of possibility). (Those interested in the details of a proof of the actual from the possible may consider a version of it here.)

Two questions remain. First, why think a divine being would be a necessary being? Second, why think a divine being is even possible?

Smith uncovers thought-provoking answers to these questions. Start with the second question: why think a divine being is even possible? A skeptic may doubt that a divine being is possible, especially if necessary existence is built into the very concept of a divine being. For suppose there is no divine being, and suppose it is part of the very concept of a divine being that such a being has necessary existence. Then by the system of logic discussed above, it follows that a divine being is impossible — for if a necessary divine being were possible, then it would actually exist, which is the very premise in question.

But, as Smith points out, necessary existence need not be contained within the concept of a divine being. We may consider instead a more minimal conception of God as an uncaused, self-sufficient creator of all else. That concept does not include necessary existence. So the present objection to the possibility of a divine being does not apply.

Moreover, Anselm is addressing skeptics who already have a coherent concept of the God whose existence they deny. There are skeptics who grant the conceptual possibility of a divine being. Thus many people, including many skeptics of a divine being, will find it intuitively plausible that the properties, being a cause of all else and being self-sufficient, are logically compatible: that is, possibly, both are instantiated together. So, although not every skeptic must accept the possibility of a divine being, minimally conceived, many do, and perhaps all may. The premise is quite modest.

What about the inference from the possibility of a divine being to its real existence? Isn’t this where the argument is bound to fail? Smith finds in Anselm an intriguing solution, which depends upon the following principle:

(C) For any essential kind of thing, if there is not, but possibly could be, something of that kind, then it is possible for something of that kind to be caused.

For example, there are not any unicorns. But let us assume that there could be. Then, according to (C), it is possible for a unicorn to be caused to exist. As Smith points out, a cause would explain the existence of a thing, and the lack of a cause would explain its non-existence. To draw this point out, consider for a moment why there aren’t any unicorns. What explains that? If unicorns were impossible, we could answer thus: because there cannot be any such things. But suppose unicorns are genuinely possible creatures. Then a different explanation is in order, and one is available: there are no unicorns because none have been caused to exist. Furthermore, there could be (or might have been) a unicorn, because a unicorn could be (or might have been) caused to exist. In short, the possibility of causing something of a certain kind explains why there could be something of that kind.

A full defense of (C) may take a book in itself. But we may say at least this much: there appear to be no identifiable counterexamples to (C), and the principle fits with everything we know about cause and effect.

Suppose we grant (C). How do we demonstrate that God exists? Here is how: Suppose there are no divine beings. And let us grant the previous premise that a divine being is possible. Then, by (C), it follows that it is possible for a divine being to be caused to exist. But a divine being, as we have been thinking of it, is just the sort of being that cannot be caused to exist: it is by its very nature a self-sufficient, uncaused Creator of all else. That sort of being can neither be created nor destroyed; otherwise, it would not be the self-sufficient cause of all else. So a contradiction follows: a divine being can be caused and cannot be caused. To escape the contradiction, we must deny the starting assumption that there are no divine beings. Therefore, there is a divine being.

Those not convinced might push back against the argument in four places. First, one might question the premise that a divine being is possible. Second, one might question principle (C). Third, one might question the premise that a divine being would be un-causable. Fourth, one might question the underlying logic that links the premises together.

Will any of these ways out work? One could reply to the third and fourth pushbacks by clarifying the meanings of the terms involved. For example, the logic behind the argument specifies a certain concept of possibility and necessity (as absolute and unalterable). And, conceiving of a divine being as uncausable is in keeping with the classic definition of God; plus, it is derivable from the Anselmean concept of a greatest thinkable being.

Pushing on (C) may be more promising. But (C) has the virtue of explaining why there can be things that do not in fact exist: they can exist because they can be caused to exist. The principle is not undeniable. But it is also not unreasonable.

One option remains: deny that a divine being is possible. Smith takes the possibility of a divine being as obvious enough, and worth entertaining at least for the sake of argument. But there is a way to become worried here. Is the possibility of a divine being more obvious than the possibility of there being no divine being? We might think neither scenario is more obviously possible than the other. Yet we are forced to choose: either there could be a divine being, or there could fail to be a divine being. If the rest of the argument is sound, then one of those options is actually impossible. Which one?

We are now at the edge of Smith’s project. I offer a final thought that may help break the stalemate. There may be a key difference between the possibility of the existence of a divine being and the possibility of its absence. In particular, when one considers the properties of a divine being, one can find it intuitively plausible, according to Smith anyway, that these properties are compatible (especially if we do not include the property of necessary existence). One’s sense of possibility here is based upon an examination of a kind of being. If so, then we have some reason to think that a divine being is possible. By contrast, when one considers the possibility of no divine being, one contemplates a lack of being, and one lacks a sense of its impossibility. This lack of sensing the impossibility of no God may tempt one into thinking there is the genuine possibility of God’s non-existence. But we should be careful. The lack of the sense that something is impossible isn’t the same as the sense that something is possible. The point, in short, is that it may be easier to sense that there could be a divine being than to sense that there could be an absence of any such being. If that seems so to you, then from the preceding premises in Anselm’s other argument, you could deduce that the scenario in which there is no divine being is actually impossible, after all.

Have we found an argument that reduces skeptics of God into unreasonable fools? Well, no; the premises are open to further inquiry and discussion. Can reason lead to God? If the above assessment is on track, then Anselm’s other argument just might be one way to make a purely reason-based belief in God possible.